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This document is designed to assist teachers by providing practical examples of real world applications of high school mathematics. Fifteen problems are presented that individuals in industry and business solve using mathematics. Each problem provides the contributor's name, suggested skills required to solve the problem, background information for solving the problem, ideas to consider in the problem-solving process, and the solution. The problem topics include: (1) straightening steel rods shipped to customers in coils; (2) laying out the horizontal alignment of a highway; (3) calculating the dimensions of unusually shaped windows; (4) calculating parking capacities on city street; (5) transmitting telephone calls; (6) adjusting a parabolic satellite antenna; (7) calculating the materials required to construct a highway; (8) calculating the forces on a bridge; (9) mounting a gas heater for optimal efficiency; (10) maximizing the efficiency of a telephone network; (11) forecasting energy needs of electrical utilities; (12) calculating the terminal velocity of a metal sphere; (13) ensuring adequate visibility at a railway crossing; (14) analyzing spot speed data to determine highway speed limits; and (15) calculating minimum area requirements that metal plates must cover in the construction of wooden trusses. (MDH)

Presents solutions to the Have a Heart problem that appeared in the February 2002 issue of this journal. (Author/NB)

Uses the Paper Balloon origami form to help students discover the relationship between ratios of corresponding distance, area, and volume measures in similar solids. (YDS)

Presents an activity on measurement and points out the importance of units which, in most cases, are omitted by students. Focuses on measurement in informal settings, indirect measurement, ratio and scales, and surface area to volume ratio. (YDS)

Assesses students' geometric thinking through an action research task that uses problems from the National Assessment of Educational Progress (NAEP). Improves students' conceptual understanding of geometric properties and measurement by exploring complex figures, perimeter, and area concepts. (YDS)

Uses the book "Spaghetti and Meatballs for All! A Mathematical Story" to help children differentiate between the mathematical concepts of perimeter and area. (KHR)

Presents a mathematics lesson that focuses on particular connections between geometry and measurement, how change in shape effects the area of the interior region of parallelograms with the same perimeter. (ASK)

Describes ways to examine leaf structure and shape using fractal geometry. Students can test hypotheses using the leaves of replicated plants to look for non-linear trends in leaf shape along the stems of plants, across species, and under different environmental growth conditions. (SAH)

Uses a discovery lesson for determining the area of an equilateral triangle given a side length as an illustration of how to introduce features of the TI-92 graphing calculator geometry package within a mathematical context. (KHR)

Explores a variety of approaches to solving one geometry problem illustrating the work of teachers, the flow of their ideas, and the diverse areas of mathematics they applied. (KHR)

Describes the process of mathematical modeling, an extensive teacher's guide, and a student modeling activity to improve the efficiency of soft-drink packaging. (KHR)

In this middle school mathematics unit two imaginary characters, Horatio and Portia, decide to make their fortune in Quincy Market (Boston, Massachusetts) running a Bull Market cart. In order to solve the problems that they encounter, they need to learn ratio and proportion, map reading, estimation, area and perimeter, population sampling, problem solving, and the collecting and processing of data. Teacher notes at the beginning of each section indicate the math objectives, materials, and whether the activity is a reinforcement or an extension of a math skill. The unit is divided into seven modules that can be used either independently or sequentially. These are: (1) an introduction to Quincy Market; (2) the use of the ruler; (3) map exploration; (4) ratio and proportion; (5) scale drawing; (6) perimeter and area; and (7) a simulation (in which the students run their business using the Bull Market Game or a computer simulation). Each module consists of two or three class activities and additional activities which can be used as extensions. The unit contains student worksheets, teacher notes, transparency masters, Bull Market Game cards, and a diskette to be used with the computer portion of the "simulation" module. (TW)

Describes a sixth-grade interdisciplinary geometry unit based on Charles Dickens's "A Christmas Carol". Focuses on finding area, volume, and perimeter, and working with estimation, decimals, and fractions in the context of making gingerbread houses. (ASK)

Uses instructional practices based on the van Hiele model to help students better conceptualize perimeter and area. (ASK)

Investigates the problem of finding all triangles that have natural-number sides for which the area is numerically equal to the perimeter. (ASK)

Provides a set of classroom activities or steps that can be used to determine the area of a triangle on a sphere. (ASK)

Presents an activity on probability and area in which students try to decide which door to buy. (ASK)

U.S. mathematics education has been criticized for being too broad. This article examines ways middle school students use simple problems and situations to foster a deeper understanding of underlying concepts. Presents a sample area and perimeter problem, describes extending the problem using tiles to determine minimum perimeter, and discusses using spreadsheets, graphs, and graphing calculators. (PEN)

Presents an activity for eighth-grade students and beyond to explore relationships between and among the areas of various polygons. Emphasizes that students should be given the opportunity to design their own examples. (ASK)

Lists questions and answers for mathematical investigations that teachers should ask when they consider using alternative approaches to teach new content. Presents an example of a mathematical investigation on concepts of area, symmetry, pattern, function, algebraic rules, and Pythagorean theorem. Argues that investigations offer opportunities for students to explore a topic in depth and to make connections among representations. (ASK)

Introduces a technique for developing tasks suitable for group investigation where students work from sets of numerical examples toward making generalizations. (ASK)

Presents a mathematical puzzle that asks about "missing" area and leads to an exploration of the Fibonacci sequence as well as genuine inquiry in plane geometry connected to algebra. Discusses the inquiry, the concepts, the solution, and an extension that deepens all students' understanding of the connections between algebra and geometry. (Author/ASK)

This activity involves students investigating the mathematics of packaging and exploring various concepts in geometry, including area and the Pythagorean theorem. Mathematics comes out of the discussion of packaging cans into six-packs and focuses on the cost-effectiveness of the horizontal storage area used. Students learn how knowledge of mathematics allows exact answers that lead to generalizations and formulas. Includes activity sheets. (PVD)

This activity for grades three through six determines how to identify the gross tonnage of a ship by measuring volume in cubic feet. During the problem-solving process, students construct and use a tool for measuring volume, derive a formula based on data collected, and compare their data with a given set of statistics. (AIM)

Presents activities that use toy balloons to offer students interesting opportunities to connect algebra and geometry. Involves students measuring the speed of a released balloon and investigating the subtle relationship between the volume of a sphere and its surface area. Prompts a rich and revealing discussion about why the experimental results are not the same as those expected theoretically. (JRH)

Presents an activity for students to investigate equal parts and area and the connection between area and fractions. Highlights the importance of such a lesson in which children explore rich mathematical ideas, share their thinking and their work with one another, and make connections to other mathematical ideas. (ASK)

Presents an activity that connects area with cutting brownies which are in different shapes for different numbers, uses algebraic equations, and fixes the exact dimensions of brownies. Concludes with four different solutions from six people for the class of 16 and a trapezoidal brownie. (ASK)

Presents an extended activity consisting of a sequence of tasks organized so that students can visit several mathematical concepts concurrently and explore connections among them. Students build solids using bendable straws to form the skeletons of various polyhedra. Topics covered include tables and charts, algebraic expressions, surface area, volume, and data analysis through measures of central tendency. Includes activity sheets. (PVD)

This investigation designed for grades three through six centers on the relationship between area and perimeter when solving a problem related to designing a garden. Goals include using area and perimeter in an authentic situation, generating hypotheses, and exploring congruence. (AIM)

Presents an activity through which students develop mathematical concepts connected to area and perimeter in a rich, real-life setting and use tables, graphs, diagrams, and spreadsheets to explore the problem, see relationships, and make and test conjectures about those relationships. Encourages algebraic thinking. (SYB)

Middle-school students were asked to determine the dimensions of a hotel atrium so that guests could enjoy the maximum area of scenic view, given that 650 feet of brass railing could be used around each floor. Several solution approaches are described. (MKR)

Explores areas of polygons by comparing polygon area to the area of the associated midpoint polygon, formed by joining the midpoints of consecutive sides. Considers triangles, quadrilaterals, pentagons, and regular polygons using paper folding, drawings on graph paper, and plexiglass MIRA constructions. (Contains 12 references.) (MKR)

Describes the effect, method, and mathematics of the following magic tricks which can be used in introducing mathematics lessons: the Ninth Card, Fibonacci Revealed, the Case of the Missing Area, I've Got Your Numbers, and the Card That Turns Inside Out. (MKR)

Recounts a sequence of activities that occurred in a senior high school geometry class and helped students to engage in creative reasoning. All student suggestions were discussed by the class, and pursuing alternative solutions was not only encouraged but required. (MKR)

Shows a way in which algebra and geometry can be used together to find the lengths and areas of spirals. This method develops better understanding of shapes, similarity, and mathematical connections in students. Discusses spirals embedded in triangles and squares, the Pythagorean theorem, and the area of regular polygons. (MKR)